Find the value of the unknown exterior angles x in the following diagrams:

(i) It is given in the question that,

1^{st} interior angle = 50^{o} and 2^{nd} interior angle = 70^{o}

*Note: According to exterior angle theorem,*

*The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.*

Exterior angle = x

Sum of interior angles = 50^{o} + 70^{o}

Thus, using exterior angle theorem,

x = 50^{o} + 70^{o}

x = 120^{o}

∴ The value of x is 120^{o}

(ii) It is given in the question that,

1^{st} interior angle = 65^{o} and 2^{nd} interior angle = 45^{o}

*Note: According to exterior angle theorem,*

*The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.*

Exterior angle = x

Sum of interior angles = 65^{o} + 45^{o}

Using, exterior angle theorem, we have

x = 65^{o} + 45^{o}

x = 110^{o}

Hence, the value of x is 110^{o}

(iii) It is given in the question that,

1^{st} interior angle = 30^{o} and 2^{nd} interior angle = 40^{o}

*Note: According to exterior angle theorem,*

*The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.*

Exterior angle = x

Sum of interior angles = 30^{o} + 40^{o}

Using exterior angle theorem, we have

x = 30^{o} + 40^{o}

x = 70^{o}

Hence, the value of x is 70^{o}

(iv) It is given in the question that,

1^{st} interior angle = 60^{o} and 2^{nd} interior angle = 60^{o}

*Note: According to exterior angle theorem,*

Exterior angle = x

Sum of interior angles = 60^{o} + 60^{o}

Using exterior angle theorem, we have

x = 60^{o} + 60^{o}

x = 120^{o}

Hence, the value of x is 120^{o}

(v) It is given in the question that,

1^{st} interior angle = 50^{o} and 2^{nd} interior angle = 50^{o}

*Note: According to exterior angle theorem:*

Exterior angle = x

Sum of interior angles = 50^{o} + 50^{o}

Using exterior angle theorem, we have

x = 50^{o} + 50^{o}

x = 100^{o}

Hence, the value of x is 100^{o}

(vi) It is given in the question that,

1^{st} interior angle = 30^{o} and 2^{nd} interior angle = 60^{o}

*Note: According to exterior angle theorem:*

Exterior angle = x

Sum of interior angles = 30^{o} + 60^{o}

Using, exterior angle theorem, we have

x = 30^{o} + 60^{o}

x = 90^{o}

Hence, the value of x is 120^{o}

3